Description

A zero curve consists of the yields to maturity for a portfolio of theoretical
zero-coupon bonds that are derived from the input Bonds
portfolio. The bootstrap method that this function uses does
not require alignment among the cash-flow dates of the
bonds in the input portfolio. It uses theoretical par bond arbitrage and yield
interpolation to derive all zero rates; specifically, the interest rates for cash
flows are determined using linear interpolation. For best results, use a portfolio
of at least 30 bonds evenly spaced across the investment horizon.

Input Arguments

Bonds — Coupon bond information to generate zero curvetable | matrix

Coupon bond information to generate zero curve, specified as a
6-column table or a n-by-2 to
n-by-6 matrix of bond
information, where the table columns or matrix columns contains:

Maturity (Column 1, Required) Maturity
date of the bond, as a serial date number. Use datenum to
convert date character vectors to serial date numbers. If
the input Bonds is a table, the
Maturity dates can be serial date
numbers, date character vectors, or datetime arrays.

EndMonthRule (Column 6, Optional)
End-of-month rule. This rule applies only when
Maturity is an end-of-month date for
a month having 30 or fewer days. 0 =
ignore rule, meaning that a bond's coupon payment date is
always the same numerical day of the month.
1 = set rule on (default),
meaning that a bond's coupon payment date is always the last
actual day of the month

:

Note

If Bonds is a table, the
Maturity dates can be serial date
numbers, date character vectors, or datetime
arrays.

If Bonds is a matrix, is an
n-by-2 to
n-by-6 matrix
where each row describes a bond, the first two columns
(Maturity and
CouponRate) are required. The
remainder of the columns are optional but must be added
in order. All rows in Bonds must have
the same number of columns.

.

Data Types: double | table

Yields — Yield to maturity of each bond in Bondsnumeric

Yield to maturity of each bond in Bonds, specified
as a N-by-1 column vector. The
number of rows (n) must match the number of rows in
Bonds.

Note

Settlement date representing time zero in derivation of zero curve,
specified as serial date number, date character vector, or datetime
array. Settle represents time zero for deriving the
zero curve, and it is normally the common settlement date for all the
bonds.

Output Arguments

ZeroRates — Implied zero rates for each point along the investment horizon defined by maturity datedecimal fractions

Implied zero rates for each point along the investment horizon defined
by a maturity date, returned as a
m-by-1 vector of decimal
fractions where m is the number of bonds with unique
maturity dates. In aggregate, the rates in ZeroRates
constitute a zero curve.

If more than one bond has the same Maturity date,
zbtyield returns the mean zero rate for that
Maturity. Any rates before the first
Maturity are assumed to be equal to the rate at
the first Maturity, that is, the curve is assumed to
be flat before the first Maturity.

Maturity dates that correspond to the ZeroRates,
returned as a m-by-1 vector of
unique maturity dates, where m is the number of bonds
of different maturity dates. These dates begin with the earliest
Maturity date and end with the latest
Maturitydate in the Bonds
table or matrix.

If either inputs for Bonds or
Settle have datetime values, then
CurveDatesCurveDates is
datetimes. Otherwise CurveDates is serial date
numbers.